Apparatus and method of fast commutation for matrix converter-based rectifier

ABSTRACT

A method of commutation in a matrix rectifier from an active vector to a zero vector includes two steps. A method of commutation in a matrix rectifier from a zero vector to an active vector includes three steps.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to matrix converters. More specifically, the present invention relates to fast commutation for the rectifiers of matrix converters.

2. Description of the Related Art

FIG. 1A is a circuit diagram showing the topology of a 3-phase-to-1-phase matrix converter, and FIG. 1B is an equivalent circuit diagram of a portion of the 3-phase-to-1-phase matrix converter shown in FIG. 1A. Each of the circuits shown in FIGS. 1A and 1B can be used either with known commutation methods discussed in this section or with the novel commutation methods according to the preferred embodiments of the present invention discussed in the Detailed Description of Preferred Embodiments section below.

In FIG. 1A, “line side” refers to the portion of the circuit on the left-hand side of the transformer T_(r) that is connected to the line voltages u_(a), u_(b), u_(c) for each of the phases A, B, C, and “load side” refers to the portion of the circuit on the right-hand side of the transformer T_(r) that is connected to the output voltage u_(o), i.e., the load. On the line side, the three-phase AC current is combined into a single-phase AC current, and on the load side, the single-phase AC current is rectified by diodes D₁ to D₄ to provide DC current.

The isolated matrix rectifier of FIG. 1A includes filter inductors L_(f) and filter capacitors C_(f) that define a line-side filter that reduces the total harmonic distortion (THD), bi-directional switches S₁ to S₆ arranged in a bridge as a 3-phase-to-1-phase matrix converter, a transformer T_(r) that provides high-voltage isolation between the line-side circuit and the load-side circuit, four diodes D₁ to D₄ arranged in a bridge to provide output rectification, an output inductor L_(o) and an output capacitor C_(o) that define a load-side filter for the output voltage. Bi-directional switches S₁ to S₆ are used in this isolated matrix rectifier to open or close the current path in either direction. As shown in FIG. 1A, the bi-directional switches S₁ to S₆ include two uni-directional switches connected in parallel. Thus, switch S_(i) in FIG. 1A corresponds to switches S_(1i) and S_(2i) in FIG. 1B, where i=1, 2, 3, 4, 5, 6.

As shown in FIG. 1A, the rectifier of the matrix converter preferably includes two parts: (1) a 3-phase-to-1-phase matrix converter and (2) a diode rectifier. The matrix converter and the diode rectifier are isolated by a high-frequency transformer T_(r). As shown in FIG. 1B, the matrix converter can be considered a reverse parallel connection of two current-source rectifiers that are labeled as converter #1 and converter #2. Converter #1 can provide a positive voltage pulse and can be referred to as a positive rectifier, and converter #2 can provide a negative voltage pulse and can be referred to as a negative rectifier.

The controller of the matrix converter turns the switches S₁ to S₆ on and off to generate a desired output voltage u_(o). One method for determining when and for how long the switches S₁ to S₆ are turned on is space-vector modulation (SVM). SVM is an algorithm for the pulse-width modulation (PWM) of the switches S₁ to S₆. That is, SVM is used to determine when the bi-directional switches S₁ to S₆ should be turned on and off. The bi-directional switches S₁ to S₆ are controlled by digital signals, e.g., either ones or zeros. Typically, a one means the switch is on, and a zero means the switch is off. In PWM, the width of the on signal, controls how long a switch is turned on, i.e., modulated. Implementations of SVM are disclosed in U.S. Application No. 62/069,815, which is hereby incorporated by reference in its entirety.

For the matrix converter shown in FIG. 1A, the switching function S_(i) can be defined as

$S_{i} = \left\{ {{\begin{matrix} {1,} & {S_{i}{turnon}} \\ {0,} & {S_{i}{turnoff}} \end{matrix}\mspace{14mu} i} \in \left\{ {1,2,3,4,5,6} \right\}} \right.$

where S_(i) is the switching function for the i^(th) switch. For example, if S₁=1, then switch S₁ is on, and if S₁=0, then switch S₁ is off.

In FIG. 1A, only two switches can be turned on at the same time to define a single current path. For example, if switches S₁ and S₆ are on, a single current path is defined between phases A and B through the transformer T_(r). If only two switches can conduct at the same time, with one switch in the top half of the bridge (S₁, S₃, S₅) and with the other switch in the bottom half of the bridge (S₂, S₄, S₆), then there are nine possible switching states as listed in Tables 1 and 2, including six active switching states and three zero switching states. In Table 1, line currents i_(a), i_(b), i_(c) are the currents in phases A, B, C, and the line-side current i_(p) is the current through the primary winding of the transformer T_(r). In Table 2, the transformer turns ratio k is assumed to be 1 so that the inductor current i_(L) is equal to the line-side current i_(p).

TABLE 1 Space Vectors, Switching States, and Phase Currents Space Switching States Vector S₁ S₂ S₃ S₄ S₅ S₆ i_(a) i_(b) i_(c) I₁ 1 0 0 0 0 1  i_(p) −i_(p) 0 I₂ 1 1 0 0 0 0  i_(p) 0 −i_(p) I₃ 0 1 1 0 0 0 0  i_(p) −i_(p) I₄ 0 0 1 1 0 0 −i_(p)  i_(p) 0 I₅ 0 0 0 1 1 0 −i_(p) 0  i_(p) I₆ 0 0 0 0 1 1 0 −i_(p)  i_(p) I₇ 1 0 0 1 0 0 0 0 0 I₈ 0 0 1 0 0 1 0 0 0 I₉ 0 1 0 0 1 0 0 0 0

TABLE 2 Space Vectors, Switching States, and Phase Currents Space Switching States Vector S₁ S₂ S₃ S₄ S₅ S₆ i_(a) i_(b) i_(c) I₁ 1 0 0 0 0 1  i_(d) −i_(d) 0 I₂ 1 1 0 0 0 0  i_(d) 0 −i_(d) I₃ 0 1 1 0 0 0 0  i_(d) −i_(d) I₄ 0 0 1 1 0 0 −i_(d)  i_(d) 0 I₅ 0 0 0 1 1 0 −i_(d) 0  i_(d) I₆ 0 0 0 0 1 1 0 −i_(d)  I_(d) I₇ 1 0 0 1 0 0 0 0 0 I₈ 0 0 1 0 0 1 0 0 0 I₉ 0 1 0 0 1 0 0 0 0

The matrix-converter's controller determines a reference current {right arrow over (I)}_(ref) and calculates the on and off times of the switches S₁ to S₆ to approximate the reference current {right arrow over (I)}_(ref) to produce the line-side currents i_(a), i_(b), and i_(c). The reference current {right arrow over (I)}_(ref) preferably is sinusoidal with a fixed frequency and a fixed magnitude: {right arrow over (I)}_(ref)={right arrow over (I)}_(ref)e^(jθ). The fixed frequency is preferably the same as the fixed frequency of each of the three-phase i_(a)(t), i_(b)(t), and i_(c)(t) to reduce harmful reflections. The controller determines the magnitude of the reference current {right arrow over (I)}_(ref) to achieve a desired output voltage u_(o). That is, the controller regulates the output voltage u_(o) by varying the magnitude of the reference current {right arrow over (I)}_(ref). Varying the magnitude of the reference current {right arrow over (I)}_(ref) changes the on and off times of the switches S₁ to S₆.

The reference current {right arrow over (I)}_(ref) moves through the α-β plane shown in FIG. 14. The angle θ is defined as the angle between the a-axis and the reference current {right arrow over (I)}_(ref). Thus, as the angle θ changes, the reference current {right arrow over (I)}_(ref) sweeps through the different sectors I-VI.

The reference current {right arrow over (I)}_(ref) can be synthesized by using combinations of the active and zero vectors. As used herein “synthesized” means that the reference current {right arrow over (I)}_(ref) can be represented as a combination of the active and zero vectors. The active and zero vectors are stationary and do not move in the α-β plane as shown in FIG. 14. The vectors used to synthesize the reference current {right arrow over (I)}_(ref) change depending on which sector the reference current {right arrow over (I)}_(ref) is located. The active vectors are chosen by the active vectors defining the sector. The zero vector is chosen for each sector by determining which on switch the two active vectors have in common and choosing the zero vector that also includes the same on switch. Using the zero vectors allows the magnitude of the line-side current i_(p) to be adjusted.

For example, consider when the current reference {right arrow over (I)}_(ref) is in sector I. The active vectors {right arrow over (I)}₁ and {right arrow over (I)}₂ define sector I. The switch S₁ is on for both active vectors {right arrow over (I)}₁ and {right arrow over (I)}₂. The zero vector {right arrow over (I)}₇ also has the switch S₁ on. Thus, when the reference current {right arrow over (I)}_(ref) is located in sector I, the active vectors {right arrow over (I)}₁ and {right arrow over (I)}₂ and zero vector {right arrow over (I)}₇ are used to synthesize the reference current {right arrow over (I)}_(ref), which provides the following equation, with the right-hand side of the equation resulting from vector {right arrow over (I)}₇ being a zero vector with zero magnitude:

${\overset{\rightarrow}{I}}_{ref} = {{{\frac{T_{1}}{T_{s}}{\overset{\rightarrow}{I}}_{1}} + {\frac{T_{2}}{T_{s}}{\overset{\rightarrow}{I}}_{2}} + {\frac{T_{7}}{T_{s}}{\overset{\rightarrow}{I}}_{7}}} = {{\frac{T_{1}}{T_{s}}{\overset{\rightarrow}{I}}_{1}} + {\frac{T_{2}}{T_{s}}{\overset{\rightarrow}{I}}_{2}}}}$

where T₁, T₂, and T₀ are the dwell times for the corresponding active switches and T_(s) is the sampling period.

The dwell time is the on time of the corresponding switches. For example, T₁ is the on time of the switches S₁ and S₆ for the active vector {right arrow over (I)}₁. Because the switch S₁ is on for each of vectors {right arrow over (I)}₁, {right arrow over (I)}₂, and {right arrow over (I)}₇, the switch S₁ is on during the entire sampling period T_(s). The ratio T₁/T_(s) is the duty cycle for the switch S₆ during the sampling period T_(s).

The sampling period T_(s) is typically chosen such that the reference current {right arrow over (I)}_(ref) is synthesized multiple times per sector. For example, the reference current {right arrow over (I)}_(ref) can be synthesized twice per sector so that the reference current {right arrow over (I)}_(ref) is synthesized twelve times per cycle, where one complete cycle is when the reference current {right arrow over (I)}_(ref) goes through sectors I-VI.

The dwell times can be calculated using the ampere-second balancing principle, i.e., the product of the reference current {right arrow over (I)}_(ref) and sampling period T_(s) equals the sum of the current vectors multiplied by the time interval of synthesizing space vectors. Assuming that the sampling period T_(s) is sufficiently small, the reference current {right arrow over (I)}_(ref) can be considered constant during the sampling period T_(s). The reference current {right arrow over (I)}_(ref) can be synthesized by two adjacent active vectors and a zero vector. For example, when the reference current {right arrow over (I)}_(ref) is in sector I, the reference current {right arrow over (I)}_(ref) can be synthesized by vectors Ī₁, {right arrow over (I)}₂, and {right arrow over (I)}₇. The ampere-second balancing equation is thus given by the following equations.

{right arrow over (I)} _(ref) T _(s) ={right arrow over (I)} ₁ T ₁ +{right arrow over (I)} ₂ T ₂ +{right arrow over (I)} ₇ T ₇

T _(s) =T ₁ +T ₂ +T ₇

where T₁, T₂, and T₇ are the dwell times for the vectors {right arrow over (I)}₁, {right arrow over (I)}₂, and {right arrow over (I)}₇ and T_(s) is sampling time. Then the dwell times are given by

T ₁ =mT _(s) sin(π/6−θ)

T ₂ =mT _(s) sin(π/6+θ)

T ₇ =T _(s) −T ₁ −T ₂

where

${m = {k\frac{I_{ref}}{i_{L}}}},$

θ is sector angle between current reference {right arrow over (I)}_(ref) and α-axis shown in FIG. 5, and k is the transformer turns ratio.

Because of the isolation provided by the transformer, the matrix-converter output voltage u₁(t) must alternate between positive and negative with high frequency to maintain the volt-sec balance. Thus, the preferred vector sequence in every sampling period T_(s) is divided into eight segments as {right arrow over (I)}_(α), {right arrow over (I)}₀, −{right arrow over (I)}_(β), {right arrow over (I)}₀, {right arrow over (I)}_(β), {right arrow over (I)}₀, −{right arrow over (I)}_(α), {right arrow over (I)}₀, where vectors {right arrow over (I)}_(α) and {right arrow over (I)}_(β) are active vectors and {right arrow over (I)}₀ is a zero vector. For example, in sector I, vectors {right arrow over (I)}_(α) and {right arrow over (I)}_(β) are active vectors {right arrow over (I)}₁ and {right arrow over (I)}₂, and vector {right arrow over (I)}₀ is zero vector {right arrow over (I)}₇. When converter #1 is active, a positive vector can be used, and when converter #2 is active, a negative vector can be used.

The waveforms of the matrix-converter output voltage u₁(t) and the matrix-converter output current i_(p)(t) during one sampling period T_(s) are shown in FIG. 5. In FIG. 5, the matrix-converter output voltage u₁(t) has three kinds of polarities:

-   -   (1) u₁(t) has positive polarity between times t₀ and t₁ and         between times t₄ and t₅. These time intervals can be referred to         as P-intervals. The current vector in a P-interval can be         referred to as a P-vector. Under the effect of a P-vector, the         matrix-converter output current i_(p)(t) increases.     -   (2) u₁(t) has negative polarity between times t₂ and t₃ and         between times t₆ and t₇. These time intervals can be referred to         as N-intervals. The current vector in a N-interval can be         referred to as a N-vector. Under the effect of an N-vector, the         matrix-converter output current i_(p)(t) decreases.     -   (3) u₁(t) is zero between times t₁ and t₂, between times t₃ and         t₄, between times t₅ and t₆, and between times t₇ and t₈. These         time intervals can be referred to as Z-intervals. The current         vector in a Z-interval can be referred to as a Z-vector. Under         the effect of a Z-vector, the absolute value of the         matrix-converter output current i_(p)(t) decreases at most to be         zero, and the direction of the matrix-converter output current         i_(p)(t) will not change during the Z-interval.

In one sampling period T_(s), the eight intervals are in sequence: P-interval, Z-interval, N-interval, Z-interval, P-interval, Z-interval, N-interval, Z-interval. As shown in FIG. 5, there is a commutation between the different intervals.

Commutation refers to turning on and off of the switches to switch from one vector to another vector. Known commutation methods for matrix converters are 4-step commutation methods based on either output current or input voltage. These known commutation methods are very complicated and require accurately measuring either the output current or the input voltage.

(1) Known 4-Step Current-Based Commutation

The 4-step current-based commutation measures the output current direction. The two-phase-to-single-phase matrix converter in FIG. 2 illustrates the problems with current-based commutation. All the important commutations can be seen in the circuit shown in FIG. 2.

As an example, assume that switches S₁₁ and S₂₁ are initially on and the switches S₁₃ and S₂₃ are initially off so that current can flow in either direction in the bi-directional switch on the left side of FIG. 2 and assume that we want to turn off the bi-directional switch on the left side of FIG. 2 and turn on the bi-directional switch on the right side of FIG. 2. As shown in FIG. 3A, when the current i>0, the following four steps can be used:

(1) switch S₁₁ turns off;

(2) switch S₂₃ turns on;

(3) switch S₂₁ turns off;

(4) switch S₁₃ turns on.

As shown in FIG. 3B, when the current i<0, the following four-step commuting method is possible:

(1) switch S₂₁ turns off;

(2) switch S₁₃ turn on;

(3) switch S₁₁ turns off;

(4) switch S₂₃ turns on.

(2) Known 4-Step Voltage-Based Commutation

Known 4-step voltage-based commutation is similar to current-based commutation. Assuming that switches S₁₁ and S₂₁ are on and switches S₁₃ and S₂₃ are off so that current can flow in either direction in the bi-directional switch on the left side of FIG. 2 and assume that the bi-directional switch on the left side of FIG. 2 is to be turned off, and the bi-directional switch on the right side of FIG. 2 is to be turned on. As shown in FIG. 4A, when voltage u_(a)>voltage u_(b), the following four steps can be used:

(1) switch S₂₃ turns on;

(2) switch S₂₁ turns off;

(3) switch S₁₃ turns on;

(4) switch S₁₁ turns off.

As shown in FIG. 4B, when the voltage u_(a)<voltage u_(b), the following four steps can be used:

(1) switch S₁₃ turns on;

(2) switch S₁₁ turns off;

(3) switch S₂₃ turns on;

(4) switch S₂₁ turns off.

Both current- and voltage-based commutation methods have problems such as taking a very long time to complete commutation, requiring complicated logic circuitry to implement the commutation methods, and requiring accurate current or voltage measurements. The frequency using these known commutation methods is limited because of the long time it takes to complete the commutation.

SUMMARY OF THE INVENTION

To overcome the problems described above, preferred embodiments of the present invention provide fast commutation. Preferred embodiments of the present invention provide 2- or 3-step commutation that achieves one or more of the following advantages:

-   -   (1) shorter time to complete commutation.     -   (2) no need to measure the output current or input voltage         because, in a rectifier-based matrix converter, the primary         current i_(p) of the transformer is well defined because the         input power factor is unity, i.e. the line-side current and         voltage are in the same phase.     -   (3) easier implementation than known 4-step commutation methods.     -   (4) suitable for high-frequency applications.

A matrix rectifier that can be used with the preferred embodiments of the present invention includes first, second, and third phases; and uni-directional switches S_(ij), where i=1, 2 and j=1, 2, 3, 4, 5, 6 and where uni-directional switches S_(1j) and S_(2j) are connected together to define first, second, third, fourth, fifth, and sixth bi-directional switches. First ends of the first, third, and fifth bidirectional switches are connected together to provide a positive-voltage node. First ends of the second, fourth, and sixth bidirectional switches are connected together to provide a negative-voltage node. Second ends of the first and fourth bidirectional switches are connected to the first phase. Second ends of the third and sixth bidirectional switches are connected to the second phase. Second ends of the fifth and second bidirectional switches are connected to the third phase. A zero vector is defined by either uni-directional switches S_(1m) and S_(1n) switched on or uni-directional switches S_(2m) and S_(2n) switched on, where (m, n)=(1, 4), (3, 6), (5, 2), and by all other uni-directional switches S_(pq) switched off, where p≠m and q≠n. An active vector is defined by either uni-directional switches S_(1m) and S_(1n) switched on or uni-directional switches S_(2m) and S_(2n) switched on, where m=1, 3, 5; n=2, 4, 6; and m, n are not connected to the same phase, and by all other uni-directional switches S_(pq) switched off, where p≠m and q≠n. Sectors I, II, III, IV, V, and VI are defined by using active vectors with (a, b)=(1, 6), (1, 2), (3, 2), (3, 4), (5, 4), and (5, 6).

According to a preferred embodiment of the present invention, a method of performing commutation in a matrix rectifier from an active vector to a zero vector includes

step (a):

-   -   for an active vector with uni-directional switches S_(1m) and         S_(1n) switched on,         -   in Sectors I, III, V, turning on uni-directional switch             S_(1x), where x is chosen such that (m, x)=(1, 4), (3, 6),             (5, 2); and         -   in Sectors II, IV, VI, turning on uni-directional switch             S_(1x), where x is chosen such that (x, n)=(1, 4), (3, 6),             (5, 2); or     -   for an active vector with uni-directional switches S_(2m) and         S_(2n) switched on,         -   in Sectors I, III, V, turning on uni-directional switch             S_(2y), where y is chosen such that (y, n)=(1, 4), (3, 6),             (5, 2); and         -   in Sectors II, IV, VI, turning on uni-directional switch             S_(2y), where y is     -   chosen such that (m, y)=(1, 4), (3, 6), (5, 2);

step (b):

-   -   for the active vector with uni-directional switches S_(1m) and         S_(1n) initially switched on,         -   in Sectors I, III, V, turning off uni-directional switch             S_(1n); and         -   in Sectors II, IV, VI, turning off uni-directional switch             S_(1m); or     -   for the active vector with uni-directional switches S_(2m) and         S_(2n) initially switched on,         -   in Sectors I, III, V, turning off uni-directional switch             S_(2m);         -   in Sectors II, IV, VI, turning off uni-directional switch             S_(2n).

Commutation is preferably performed by measuring input voltage and without measuring output current or output voltage.

According to a preferred embodiment of the present invention, a method of operating a matrix rectifier includes performing commutation from an active vector to a zero vector using the commutation method according to various other preferred embodiments of the present invention and modulating the first, second, third, fourth, fifth, and sixth bi-directional switches based on space vector modulation.

According to a preferred embodiment of the present invention, a method of performing commutation in a matrix rectifier from a zero vector to an active vector includes:

step (a):

-   -   for a zero vector with uni-directional switches S_(1m) and         S_(1n) switched on,         -   in Sectors I, III, V, turning on uni-directional switch             S_(1x), where x=1, 3, 5 and x is chosen such that a negative             voltage is provided at the positive-voltage node; and         -   in Sectors II, IV, VI, turning on uni-directional switch             S_(1x), where x=2, 4, 6 and x is chosen such that a positive             voltage is provided at the negative-voltage node; or     -   for a zero vector with uni-directional switches S_(2m) and         S_(2n) switched on,         -   in Sectors I, III, V, turning on uni-directional switch             S_(2y), where y=2, 4, 6 and y is chosen such that a positive             voltage is provided at the negative-voltage node; and         -   in Sectors II, IV, VI, turning on uni-directional switch             S_(2y), where y=1, 3, 5 and y is chosen such that a negative             voltage is provided at the positive-voltage node;

step (b):

-   -   for the zero vector with uni-directional switches S_(1m) and         S_(1n) initially switched on,         -   in Sectors I, III, V, turning off uni-directional switch             S_(1m); and         -   in Sectors II, IV, VI, turning off uni-directional switch             S_(1n); or     -   for the zero vector with uni-directional switches S_(2m) and         S_(2n) initially switched on,         -   in Sectors I, III, V, turning off uni-directional switch             S_(2n); and         -   in Sectors II, IV, VI, turning off uni-directional switch             S_(2m); and

step (c):

-   -   for the zero vector with uni-directional switches S_(1m) and         S_(1n) initially switched on,         -   in Sectors I, III, V, turning off uni-directional switches             S_(1x) and S_(1n) and turning on uni-directional switches             S_(2x) and S_(2n); and         -   in Sectors II, IV, VI, turning off uni-directional switches             S_(1x) and S_(1m) and turning on uni-directional switches             S_(2x) and S_(2m); or     -   for the zero vector with uni-directional switches S_(2m) and         S_(2n) initially switched on,         -   in Sectors I, III, V, turning off uni-directional switches             S_(2m) and S_(2y) and turning on uni-directional switches             S_(1m) and S_(1y); and         -   in Sectors II, IV, VI, turning off uni-directional switches             S_(2n) and S_(2y) and turning on uni-directional switches             S_(1n) and S_(1y).

Commutation is preferably performed by measuring input voltage and without measuring output current or output voltage. Preferably, in step (a), for the zero vector with uni-directional switches S_(1m) and S_(1n) initially switched on, no current passes through uni-directional switch S_(1x); or for the zero vector with uni-directional switches S_(2m) and S_(2n) initially switched on, no current passes through uni-directional switch S_(2y). Preferably, step (b) lasts until a current through the positive-voltage node or the negative-voltage node reaches zero. The method further preferably includes a transformer connected to the positive-voltage and negative-voltage nodes, where a holding time Δt of step (b) is provided by:

${\Delta \; t} = \frac{L_{o}I_{1\; \max}}{U_{1\; \min}}$

where I_(1max) is a maximum current of the matrix converter, U_(1min) is a minimum output voltage of the matrix converter, and L_(o) is a leakage inductance of the transformer.

According to a preferred embodiment of the present invention, a method of operating a matrix rectifier includes performing commutation from a zero vector to an active vector using the commutation method according to various other preferred embodiments of the present invention and modulating the first, second, third, fourth, fifth, and sixth bi-directional switches based on space vector modulation.

Preferably, gate signals s_(ij) applied to uni-directional switches S_(ij) are generated by determining a space-vector-modulation sector and generating:

-   -   a carrier signal;     -   first, second, and third comparison signals based on dwell times         of corresponding zero vector and two active vectors of the         space-vector-modulation sector;     -   modulation signals s_(i) corresponding to the first, second,         third, fourth, fifth, and sixth bi-directional switches based on         the comparison of the carrier signal and the first, second, and         third comparison signals, where i=1, 2, 3, 4, 5, 6;     -   first converter select signal SelectCon1 and second converter         select signal SelectCon2 based on if a positive or a negative         voltage is outputted; wherein the gate signals s_(ij) are         generated based on:

s _(1j) =s _(i)×SelectCon1(j=1,3,5,4,6,2)

s _(2j) =s _(i)×SelectCon2(j=1,3,5,4,6,2).

The above and other features, elements, characteristics, steps, and advantages of the present invention will become more apparent from the following detailed description of preferred embodiments of the present invention with reference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are circuit diagrams of matrix-converters.

FIG. 2 is a circuit diagram of a two-phase-to-single-phase matrix converter.

FIGS. 3A and 3B show the steps of current-based commutation.

FIGS. 4A and 4B show the steps of voltage-based commutation.

FIG. 5 shows the waveforms of the rectifier of a matrix converter.

FIG. 6 shows eight switching modes in one sampling period in sector I.

FIGS. 7A and 7B show 2-step commutation from an active vector to a zero vector for a positive current in sector I.

FIGS. 8A and 8B show 3-step commutation from a zero vector to an active vector.

FIG. 9 is a block diagram of gate-signal generator.

FIG. 10 shows SVM-modulation and commutation signals in one sampling period.

FIG. 11 shows gate signals in one sampling period in sector I.

FIG. 12 shows 2-step commutation at time t₂.

FIG. 13 shows 3-step commutation at time t₃.

FIG. 14 shows a current-space vector hexagon.

FIG. 15 shows 2-step commutation from an active vector to a zero vector for a negative current in sector I.

FIG. 16 shows 3-step commutation from a zero vector to an active vector for a negative current in sector I.

FIG. 17 shows 2-step commutation from an active vector to a zero vector for a positive current in sector II.

FIG. 18 shows 3-step commutation from a zero vector to an active vector for a positive current in sector II.

FIG. 19 shows 2-step commutation from an active vector to a zero vector for a negative current in sector II.

FIG. 20 shows 3-step commutation from a zero vector to an active vector for a negative current in sector II.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Preferred embodiments of the present invention improve the known four-step commutation methods. Current commutation can ensure reliable operation. Because the rectifiers of 3-phase-to-1-phase matrix-converters have a different structure compared to the rectifiers of known 3-phase-to-3-phase matrix converters, rectifiers of a 3-phase-to-1-phase matrix-converter can use a different current-based commutation method, as discussed below.

As shown in FIG. 5, the matrix-converter output current i_(p)(t) is positive in adjacent P- and Z-intervals, except for the commutation area, and the matrix-converter output current i_(p)(t) is negative in adjacent N- and Z-intervals, except for the commutation area. During adjacent P- and Z-intervals, converter #1 works normally and converter #2 stops working, and in contrast, during adjacent N- and Z-intervals, converter #2 works normally and converter #1 stops working. Thus, there are eight switching modes in one sampling period exclusive of the commutation areas as shown in FIG. 6. In one sampling period, there are two types of current-based commutations: (1) active vector (i.e., either P-vector or N-vector) to zero vector and (2) zero vector to active vector. A two-step active-vector-to-zero-vector commutation and a three-step zero-vector-to-active-vector commutation are discussed below.

(1) Active Vector to Zero Vector (P-Vector to Z-Vector or N-Vector to Z-Vector)

As seen in FIGS. 5 and 6, active-vector-to-zero-vector commutations include the commutations from mode 1 (P-vector) to mode 2 (Z-vector), mode 3 (N-vector) to mode 4 (Z-vector), mode 5 (P-vector) to mode 6 (Z-vector), and mode 7 (N-vector) to mode 8 (Z-vector). During active-vector-to-zero-vector commutation, the direction of the output current of the rectifier of the matrix converter does not change. Thus, active-vector-to-zero-vector commutation only adds an overlap time just as the commutation method of the current-source inverter. The overlap time is added to make sure that the current can smoothly transition from one switch to another switch and that no overvoltage is induced during this transition. The overlap time is determined by the “turn on” and “turn off” speed of these two switches. For example, as shown in FIGS. 7A and 7B, the commutation from mode 1 to mode 2 only has two steps:

(1) switch S₁₄ turns on, and

(2) switch S₁₆ turns off.

Thus, commutation from an active vector to a zero vector is achieved. FIGS. 7A and 7B show an example of the 2-step commutation from an active vector to a zero vector for a positive current in sector I. Similar commutation steps are performed in sectors III and V.

FIG. 15 shows a 2-step commutation from an active vector to a zero vector for a negative current in sector I. The commutation steps include:

(1) switch S₂₁ turns on, and

(2) switch S₂₃ turns off.

Similar commutation steps are performed in sectors III and V.

FIG. 17 shows a 2-step commutation from an active vector to a zero vector for a positive current in sector II. The commutation steps include:

(3) switch S₁₅ turns on, and

(4) switch S₁₁ turns off.

Similar commutation steps are performed in sectors IV and VI.

FIG. 19 shows a 2-step commutation from an active vector to a zero vector for a negative current in sector II. The commutation steps include:

(1) switch S₂₂ turns on, and

(2) switch S₂₄ turns off.

Similar commutation steps are performed in sectors IV and VI.

(2) Zero Vector to Active Vector (Z-Vector to P-Vector or Z-Vector to N-Vector)

As seen in FIGS. 5 and 6, zero-vector-to-active-vector commutations include the commutations from mode 2 (Z-vector) to mode 3 (N-vector), mode 4 (Z-vector) to mode 5 (P-vector), mode 6 (Z-vector) to mode 7 (N-vector), and mode 8 (Z-vector) to mode 1 of the next sampling period (P-vector). During zero-vector-to-active-vector commutation, the direction of the output current of the rectifier of the matrix converter changes. Thus, zero-vector-to-active-vector commutation requires an additional step. For example, as shown in FIGS. 8A and 8B, the commutation from mode 2 to mode 3 in sector I includes three steps:

-   -   (1) switch S₁₅ turns on. The purpose of this step is to provide         a current path for the next step. Although switch S₁₅ is on in         this step, there is no current passing through switch S₁₅         because the voltage u_(a) is larger than the voltage u_(c) and         because the diode in series with the switch S₁₅ is reversed         biased. The output vector is still the Z-vector. The time span         Δt₁ that this step maintains can be decided according to the         overlap time of the current-source inverter. The overlap time is         added to make sure that the switch S₁₅ is on before switch S₁₁         turns off, considering the delay between the gate signals of the         switches S₁₁ and S₁₅.     -   (2) Switch S₁₁ turns off. After turning switch S₁₁ off, the         output vector is substantially the N-vector, so the output         current will be reduced sharply and reach zero quickly. This         step should last long enough to ensure that the current reaches         zero. The holding time Δt₂ of this step can be estimated by the         maximum current I_(1max) of the matrix converter, the minimum         output voltage U_(1min) of the matrix converter, and the leakage         inductance L_(o) of the transformer:

$\begin{matrix} {{\Delta \; t_{2}} = \frac{L_{O}I_{1\; \max}}{U_{1\; \min}}} & (1) \end{matrix}$

-   -   -   For simplicity, the holding time Δt₂ can be selected as a             fixed value according to eq. (1). The holding time Δt₂ is             determined by the transition time required for the output             current to reach zero. The holding time Δt₂ based on eq. (1)             is long enough to ensure that the current reaches zero under             all the conditions.

    -   (3) Switches S₁₅ and S₁₄ turn off and switches S₂₄ and S₂₄ turn         on.         Thus, commutation from a zero vector to an active vector is         achieved. FIGS. 8A and 8B show an example of the 3-step         commutation from a zero vector to an active vector for a         positive current in sector I. Similar commutation steps are         performed in sectors III and V.

FIG. 16 shows a 3-step commutation from a zero vector to an active vector for a negative current in sector I. The commutation steps include:

(1) switch S₂₂ turns on,

(2) switch S₂₄ turns off, and

(3) switches S₂₁ and S₂₂ turn off and switches S₁₁ and S₁₂ turn on.

Similar commutation steps are performed in sectors III and V.

FIG. 18 shows a 3-step commutation from a zero vector to an active vector for a positive current in sector II. The commutation steps include:

(1) switch S₁₆ turns on,

(2) switch S₁₂ turns off, and

(3) switches S₁₅ and S₁₆ turn off and switches S₂₅ and S₂₆ turn on.

Similar commutation steps are performed in sectors IV and VI.

FIG. 20 shows a 3-step commutation from a zero vector to an active vector for a negative current in sector II. The commutation steps include:

(1) switch S₂₃ turns on,

(2) switch S₂₅ turns off, and

(3) switches S₂₃ and S₂₂ turn off and switches S₁₃ and S₁₂ turn on.

Similar commutation steps are performed in sectors IV and VI.

As shown in FIG. 10, the time periods (or “effective area” in FIG. 10) when only converter #1 is on and the time periods when only converter #2 is on are separate from each other. In FIG. 10, the signal SelectCon1 is 1 when converter #1 is on, i.e., the effective area for converter #1, and is 0 when converter #1 is off, i.e., the effective area for converter #2. Similarly, the signal SelectCon2 when converter #2 is on, i.e., the effective area for converter #2, and is 0 when converter #2 is off, i.e., the effective area for converter #1. As shown in FIG. 9, the following three steps can be used to achieve modulation and commutation.

(1) Generate the Signals S_(i) (i=1, 2, 3, 4, 5, 6)

Accordingly, a carrier signal and three compare value signals CMP0, CMP1, CMP2 are used to generate the SVM PWM signals S_(i)′ (i=1, 2, 3, 4, 5, 6). The compare values signals CMP0, CMP1, CMP2 are determined by the dwell time of each vector. After the holding time Δt₁ for the falling edge of signals S_(i)′ has lapsed, the signals S_(i) (i=1, 2, 3, 4, 5, 6) can be generated. The falling edge of signal S_(i) is delayed for holding time Δt₁ compared with the signal S_(i)′. An overlap time is added to the signals S₁, S₃, S₅, and S₄, S₆, S₂ just as in the commutation method of the current-source inverter. In sector I, for example, the signals S₁, S₃, S₅ and S₄, S₆, S₂ are shown in FIG. 10.

(2) Generate Signal SelectCon1 and Signal SelectCon2

After comparison between the carrier signal and CMP1 and the delay Δt of both rising and falling edges, signal SelectCon1 can be generated, as shown in FIGS. 9 and 10. The fixed delay time Δt is based on the three steps of zero-vector-to-active-vector commutation. So the delay time Δt can be determined by eq. (2).

Δt=Δt _(t) +Δt ₂  (2)

where Δt₁ is the overlap time and Δt₂ is estimated by eq. (1).

(3) Generate Gate Signals S_(i1) for Converter #1 and Gate Signals S_(i2) for Converter #2

The gate signals S_(1j) for converter #1 can be generated by eq. (3), and the gate signals S_(2j) for converter #2 can be generated by eq. (4):

S _(1j) =S _(j)×SelectCon1(j=1,3,5,4,6,2)  (3)

S _(2j) =S _(j)×SelectCon2(j=1,3,5,4,6,2)  (4)

For example, in sector I, the gate signals S₁₁, S₁₃, S₁₅, S₁₄, S₁₆, and S₁₂ are generated for converter #1, and the gate signals S₂₁, S₂₃, S₂₂, S₂₄, S₂₆, and S₂₂ are generated for converter #1 as shown in FIG. 10.

FIGS. 11-13 show the gate signals generated using a field programmable gate array (FPGA) to implement the method described above. FIG. 11 shows the gate signals for switches S₁ to S₆ in sector I. The time period from time t₁ to time t₉ is one sampling period T_(s). Times t₂, t₄, t₆, and t₈ use 2-step commutation, and times t₁, t₂, t₃, t₇, and t₉ use 3-step commutation.

For example, at time t₂, the commutation from mode 1 to mode 2 (from active vector to zero vector) as shown in FIG. 7 is in two steps. The 2-step commutation waveforms are shown in FIG. 12. At time t₃, the commutation from mode 2 to mode 3 (from zero vector to active vector) as shown in FIG. 8 is in three steps. The 3-step commutation waveforms are shown in FIG. 13.

It should be understood that the foregoing description is only illustrative of the present invention. Various alternatives and modifications can be devised by those skilled in the art without departing from the present invention. Accordingly, the present invention is intended to embrace all such alternatives, modifications, and variances that fall within the scope of the appended claims. 

What is claimed is:
 1. A method of performing commutation in a matrix rectifier from an active vector to a zero vector, the matrix rectifier includes: first, second, and third phases; and uni-directional switches S_(ij), where i=1, 2 and j=1, 2, 3, 4, 5, 6 and where uni-directional switches S_(1j) and S_(2j) are connected together to define first, second, third, fourth, fifth, and sixth bi-directional switches; wherein first ends of the first, third, and fifth bidirectional switches are connected together to provide a positive-voltage node; first ends of the second, fourth, and sixth bidirectional switches are connected together to provide a negative-voltage node; second ends of the first and fourth bidirectional switches are connected to the first phase; second ends of the third and sixth bidirectional switches are connected to the second phase; second ends of the fifth and second bidirectional switches are connected to the third phase; a zero vector is defined by either uni-directional switches S_(1m) and S_(1n) switched on or uni-directional switches S_(2m) and S_(2n) switched on, where (m, n)=(1, 4), (3, 6), (5, 2), and by all other uni-directional switches S_(pq) switched off, where p≠m and q≠n; and an active vector is defined by either uni-directional switches S_(1m) and S_(1n) switched on or uni-directional switches S_(2m) and S_(2n) switched on, where m=1, 3, 5; n=2, 4, 6; and m, n are not connected to the same phase, and by all other uni-directional switches S_(pq) switched off, where p≠m and q≠n; Sectors I, II, III, IV, V, and VI are defined by using active vectors with (a, b)=(1, 6), (1, 2), (3, 2), (3, 4), (5, 4), and (5, 6); the method comprising: step (a): for an active vector with uni-directional switches S_(1m) and S_(1n) switched on, in Sectors I, III, V, turning on uni-directional switch S_(1x), where x is chosen such that (m, x)=(1, 4), (3, 6), (5, 2); and in Sectors II, IV, VI, turning on uni-directional switch S_(1x), where x is chosen such that (x, n)=(1, 4), (3, 6), (5, 2); or for an active vector with uni-directional switches S_(2m) and S_(2n) switched on, in Sectors I, III, V, turning on uni-directional switch S_(2y), where y is chosen such that (y, n)=(1, 4), (3, 6), (5, 2); and in Sectors II, IV, VI, turning on uni-directional switch S_(2y), where y is chosen such that (m, y)=(1, 4), (3, 6), (5, 2); step (b): for the active vector with uni-directional switches S_(1m) and S_(1n) initially switched on, in Sectors I, III, V, turning off uni-directional switch S_(1n); and in Sectors II, IV, VI, turning off uni-directional switch S_(1m); or for the active vector with uni-directional switches S_(2m) and S_(2n) initially switched on, in Sectors I, III, V, turning off uni-directional switch S_(2m); in Sectors II, IV, VI, turning off uni-directional switch S_(2n).
 2. The method of claim 1, wherein commutation is performed by measuring input voltage and without measuring output current or output voltage.
 3. A method of operating a matrix rectifier comprising: performing commutation from an active vector to a zero vector using the method of claim 1; and modulating the first, second, third, fourth, fifth, and sixth bi-directional switches based on space vector modulation.
 4. The method of claim 3, wherein gate signals s_(ij) applied to uni-directional switches S_(ij) are generated by: determining a space-vector-modulation sector; and generating: a carrier signal; first, second, and third comparison signals based on dwell times of corresponding zero vector and two active vectors of the space-vector-modulation sector; modulation signals s_(j) corresponding to the first, second, third, fourth, fifth, and sixth bi-directional switches based on the comparison of the carrier signal and the first, second, and third comparison signals, where j=1, 2, 3, 4, 5, 6; first converter select signal SelectCon1 and second converter select signal SelectCon2 based on if a positive or a negative voltage is outputted; wherein the gate signals s_(ij) are generated based on: s _(1j) =s _(j)×SelectCon1(j=1,3,5,4,6,2) s _(2j) =s _(j)×SelectCon2(j=1,3,5,4,6,2).
 5. A method of performing commutation in a matrix rectifier from a zero vector to an active vector, the matrix rectifier includes: first, second, and third phases; and uni-directional switches S_(ij), where i=1, 2 and j=1, 2, 3, 4, 5, 6 and where uni-directional switches S_(1j) and S_(2j) are connected together to define first, second, third, fourth, fifth, and sixth bi-directional switches; wherein first ends of the first, third, and fifth bidirectional switches are connected together to provide a positive-voltage node; first ends of the second, fourth, and sixth bidirectional switches are connected together to provide a negative-voltage node; second ends of the first and fourth bidirectional switches are connected to the first phase; second ends of the third and sixth bidirectional switches are connected to the second phase; second ends of the fifth and second bidirectional switches are connected to the third phase; a zero vector is defined by either uni-directional switches S_(1m) and S_(1n) switched on or uni-directional switches S_(2m) and S_(2n) switched on, where (m, n)=(1, 4), (3, 6), (5, 2), and by all other uni-directional switches S_(pq) switched off, where p≠m and q≠n; an active vector is defined by either uni-directional switches S_(1m) and S_(1n) switched on or uni-directional switches S_(2m) and S_(2n) switched on, where m=1, 3, 5; n=2, 4, 6; and m, n are not connected to the same phase, and by all other uni-directional switches S_(pq) switched off, where p≠m and q≠n; and Sectors I, II, III, IV, V, and VI are defined by using active vectors with (a, b)=(1, 6), (1, 2), (3, 2), (3, 4), (5, 4), and (5, 6); the method comprising: step (a): for a zero vector with uni-directional switches S_(1m) and S_(1n) switched on, in Sectors I, III, V, turning on uni-directional switch S_(1x), where x=1, 3, 5 and x is chosen such that a negative voltage is provided at the positive-voltage node; and in Sectors II, IV, VI, turning on uni-directional switch S_(1x), where x=2, 4, 6 and x is chosen such that a positive voltage is provided at the negative-voltage node; or for a zero vector with uni-directional switches S_(2m) and S_(2n) switched on, in Sectors I, III, V, turning on uni-directional switch S_(2y), where y=2, 4, 6 and y is chosen such that a positive voltage is provided at the negative-voltage node; and in Sectors II, IV, VI, turning on uni-directional switch S_(2y), where y=1, 3, 5 and y is chosen such that a negative voltage is provided at the positive-voltage node; step (b): for the zero vector with uni-directional switches S_(1m) and S_(1n) initially switched on, in Sectors I, III, V, turning off uni-directional switch S_(1m); and in Sectors II, IV, VI, turning off uni-directional switch S_(1n); or for the zero vector with uni-directional switches S_(2m) and S_(2n) initially switched on, in Sectors I, III, V, turning off uni-directional switch S_(2n); and in Sectors II, IV, VI, turning off uni-directional switch S_(2m); and step (c): for the zero vector with uni-directional switches S_(1m) and S_(1n) initially switched on, in Sectors I, III, V, turning off uni-directional switches S_(1x) and S_(1n) and turning on uni-directional switches S_(2x) and S_(2n); and in Sectors II, IV, VI, turning off uni-directional switches S_(1x) and S_(1m) and turning on uni-directional switches S_(2x) and S_(2m); or for the zero vector with uni-directional switches S_(2m) and S_(2n) initially switched on, in Sectors I, III, V, turning off uni-directional switches S_(2m) and S_(2y) and turning on uni-directional switches S_(1m) and S_(1y); and in Sectors II, IV, VI, turning off uni-directional switches S_(2n) and S_(2y) and turning on uni-directional switches S_(1n) and S_(1y).
 6. The method of claim 5, wherein commutation is performed by measuring input voltage and without measuring output current or output voltage.
 7. The method of claim 5, wherein in step (a): for the zero vector with uni-directional switches S_(1m) and S_(1n) initially switched on, no current passes through uni-directional switch S_(1x); or for the zero vector with uni-directional switches S_(2m) and S_(2n) initially switched on, no current passes through uni-directional switch S_(2y).
 8. The method of claim 5, wherein step (b) lasts until a current through the positive-voltage node or the negative-voltage node reaches zero.
 9. The method of claim 5, further comprising a transformer connected to the positive-voltage and negative-voltage nodes; wherein a holding time Δt of step (b) is provided by: ${\Delta \; t} = \frac{L_{O}I_{1\; \max}}{U_{1\; \min}}$ where I_(1max) is a maximum current of the matrix converter, U_(1min) is a minimum output voltage of the matrix converter, and L_(o) is a leakage inductance of the transformer.
 10. A method of operating a matrix rectifier comprising: performing commutation from a zero vector to an active vector using the method of claim 5; and modulating the first, second, third, fourth, fifth, and sixth bi-directional switches based on space vector modulation.
 11. The method of claim 10, wherein gate signals s_(ij) applied to uni-directional switches S⁻ _(ij) are generated by: determining a space-vector-modulation sector; generating: a carrier signal; first, second, and third comparison signals based on dwell times of corresponding zero vector and two active vectors of the space-vector-modulation sector; modulation signals s_(j) corresponding to the first, second, third, fourth, fifth, and sixth bi-directional switches based on the comparison of the carrier signal and the first, second, and third comparison signals, where j=1, 2, 3, 4, 5, 6; and first converter select signal SelectCon1 and second converter select signal SelectCon2 based on if a positive or a negative voltage is outputted; wherein the gate signals s_(ij) are generated based on: s _(1j) =s _(j)×SelectCon1(j=1,3,5,4,6,2) s _(2j) =s _(j)×SelectCon2(j=1,3,5,4,6,2). 